Continuity of attractors for parabolic problems with localized large diffusion

In this paper we study the continuity of asymptotics of semilinear parabolic problems of the form u(t) - div(p(x)del u) + lambda u =f(u) in a bounded smooth domain ohm subset of R `` with Dirichlet boundary conditions when the diffusion coefficient p becomes large in a subregion ohm(0) which is interior to the physical domain ohm. We prove, under suitable assumptions, that the family of attractors behave upper and lower semicontinuously as the diffusion blows up in ohm(0). (c) 2006 Elsevier Ltd. All rights reserved.

A Mass-Conserving Algorithm for Dynamical Lubrication Problems With Cavitation

A numerical algorithm for fully dynamical lubrication problems based on the Elrod-Adams formulation of the Reynolds equation with mass-conserving boundary conditions is described. A simple but effective relaxation scheme is used to update the solution maintaining the complementarity conditions on the variables that represent the pressure and fluid fraction. The equations of motion are discretized in time using Newmark`s scheme, and the dynamical variables are updated within the same relaxation process just mentioned. The good behavior of the proposed algorithm is illustrated in two examples: an oscillatory squeeze flow (for which the exact solution is available) and a dynamically loaded journal bearing. This article is accompanied by the ready-to-compile source code with the implementation of the proposed algorithm. [DOI: 10.1115/1.3142903]

A discontinuous-Galerkin-based immersed boundary method with non-homogeneous boundary conditions and its application to elasticity

We propose a discontinuous-Galerkin-based immersed boundary method for elasticity problems. The resulting numerical scheme does not require boundary fitting meshes and avoids boundary locking by switching the elements intersected by the boundary to a discontinuous Galerkin approximation. Special emphasis is placed on the construction of a method that retains an optimal convergence rate in the presence of non-homogeneous essential and natural boundary conditions. The role of each one of the approximations introduced is illustrated by analyzing an analog problem in one spatial dimension. Finally, extensive two- and three-dimensional numerical experiments on linear and nonlinear elasticity problems verify that the proposed method leads to optimal convergence rates under combinations of essential and natural boundary conditions. (C) 2009 Elsevier B.V. All rights reserved.

A discontinuous-Galerkin-based immersed boundary method

A numerical method to approximate partial differential equations on meshes that do not conform to the domain boundaries is introduced. The proposed method is conceptually simple and free of user-defined parameters. Starting with a conforming finite element mesh, the key ingredient is to switch those elements intersected by the Dirichlet boundary to a discontinuous-Galerkin approximation and impose the Dirichlet boundary conditions strongly. By virtue of relaxing the continuity constraint at those elements. boundary locking is avoided and optimal-order convergence is achieved. This is shown through numerical experiments in reaction-diffusion problems. Copyright (c) 2008 John Wiley & Sons, Ltd.

Cascades of Hopf bifurcations from boundary delay

We consider a 1-dimensional reaction-diffusion equation with nonlinear boundary conditions of logistic type with delay. We deal with non-negative solutions and analyze the stability behavior of its unique positive equilibrium solution, which is given by the constant function u equivalent to 1. We show that if the delay is small, this equilibrium solution is asymptotically stable, similar as in the case without delay. We also show that, as the delay goes to infinity, this equilibrium becomes unstable and undergoes a cascade of Hopf bifurcations. The structure of this cascade will depend on the parameters appearing in the equation. This equation shows some dynamical behavior that differs from the case where the nonlinearity with delay is in the interior of the domain. (C) 2009 Elsevier Inc. All rights reserved.

Efficient solutions to robust, semi-implicit discretizations of the immersed boundary method

The immersed boundary method is a versatile tool for the investigation of flow-structure interaction. In a large number of applications, the immersed boundaries or structures are very stiff and strong tangential forces on these interfaces induce a well-known, severe time-step restriction for explicit discretizations. This excessive stability constraint can be removed with fully implicit or suitable semi-implicit schemes but at a seemingly prohibitive computational cost. While economical alternatives have been proposed recently for some special cases, there is a practical need for a computationally efficient approach that can be applied more broadly. In this context, we revisit a robust semi-implicit discretization introduced by Peskin in the late 1970s which has received renewed attention recently. This discretization, in which the spreading and interpolation operators are lagged. leads to a linear system of equations for the inter-face configuration at the future time, when the interfacial force is linear. However, this linear system is large and dense and thus it is challenging to streamline its solution. Moreover, while the same linear system or one of similar structure could potentially be used in Newton-type iterations, nonlinear and highly stiff immersed structures pose additional challenges to iterative methods. In this work, we address these problems and propose cost-effective computational strategies for solving Peskin`s lagged-operators type of discretization. We do this by first constructing a sufficiently accurate approximation to the system`s matrix and we obtain a rigorous estimate for this approximation. This matrix is expeditiously computed by using a combination of pre-calculated values and interpolation. The availability of a matrix allows for more efficient matrix-vector products and facilitates the design of effective iterative schemes. We propose efficient iterative approaches to deal with both linear and nonlinear interfacial forces and simple or complex immersed structures with tethered or untethered points. One of these iterative approaches employs a splitting in which we first solve a linear problem for the interfacial force and then we use a nonlinear iteration to find the interface configuration corresponding to this force. We demonstrate that the proposed approach is several orders of magnitude more efficient than the standard explicit method. In addition to considering the standard elliptical drop test case, we show both the robustness and efficacy of the proposed methodology with a 2D model of a heart valve. (C) 2009 Elsevier Inc. All rights reserved.

ON THE SUPERCRITICALITY OF THE FIRST HOPF BIFURCATION IN A DELAY BOUNDARY PROBLEM

The goal of this paper is to analyze the character of the first Hopf bifurcation (subcritical versus supercritical) that appears in a one-dimensional reaction-diffusion equation with nonlinear boundary conditions of logistic type with delay. We showed in the previous work [Arrieta et al., 2010] that if the delay is small, the unique non-negative equilibrium solution is asymptotically stable. We also showed that, as the delay increases and crosses certain critical value, this equilibrium becomes unstable and undergoes a Hopf bifurcation. This bifurcation is the first one of a cascade occurring as the delay goes to infinity. The structure of this cascade will depend on the parameters appearing in the equation. In this paper, we show that the first bifurcation that occurs is supercritical, that is, when the parameter is bigger than the delay bifurcation value, stable periodic orbits branch off from the constant equilibrium.

Reaction-diffusion systems coupled at the boundary and the Morse-Smale property

We study an one-dimensional nonlinear reaction-diffusion system coupled on the boundary. Such system comes from modeling problems of temperature distribution on two bars of same length, jointed together, with different diffusion coefficients. We prove the transversality property of unstable and stable manifolds assuming all equilibrium points are hyperbolic. To this end, we write the system as an equation with noncontinuous diffusion coefficient. We then study the nonincreasing property of the number of zeros of a linearized nonautonomous equation as well as the Sturm-Liouville properties of the solutions of a linear elliptic problem. (C) 2008 Elsevier Inc. All rights reserved.

Statistical bound of genetic solutions to quadratic assignment problems

Quadratic assignment problems (QAPs) are commonly solved by heuristic methods, where the optimum is sought iteratively. Heuristics are known to provide good solutions but the quality of the solutions, i.e., the confidence interval of the solution is unknown. This paper uses statistical optimum estimation techniques (SOETs) to assess the quality of Genetic algorithm solutions for QAPs. We examine the functioning of different SOETs regarding biasness, coverage rate and length of interval, and then we compare the SOET lower bound with deterministic ones. The commonly used deterministic bounds are confined to only a few algorithms. We show that, the Jackknife estimators have better performance than Weibull estimators, and when the number of heuristic solutions is as large as 100, higher order JK-estimators perform better than lower order ones. Compared with the deterministic bounds, the SOET lower bound performs significantly better than most deterministic lower bounds and is comparable with the best deterministic ones. 

On statistical bounds of heuristic solutions to location problems

Solutions to combinatorial optimization problems, such as problems of locating facilities, frequently rely on heuristics to minimize the objective function. The optimum is sought iteratively and a criterion is needed to decide when the procedure (almost) attains it. Pre-setting the number of iterations dominates in OR applications, which implies that the quality of the solution cannot be ascertained. A small, almost dormant, branch of the literature suggests using statistical principles to estimate the minimum and its bounds as a tool to decide upon stopping and evaluating the quality of the solution. In this paper we examine the functioning of statistical bounds obtained from four different estimators by using simulated annealing on p-median test problems taken from Beasley’s OR-library. We find the Weibull estimator and the 2nd order Jackknife estimator preferable and the requirement of sample size to be about 10 being much less than the current recommendation. However, reliable statistical bounds are found to depend critically on a sample of heuristic solutions of high quality and we give a simple statistic useful for checking the quality. We end the paper with an illustration on using statistical bounds in a problem of locating some 70 distribution centers of the Swedish Post in one Swedish region. 

How initial vocational education and training (IVET) teachers in Sweden perceive their prospects of being able to prepare upper secondary school pupils for a future occupation

Vocational teachers in Swedish upper secondary schools are a heterogeneous category of teachers, connected to different types of trade. These teachers represent a broad set of trade skills varying in content and character. In their teacher role, they continue to wear the clothes, speak the language, share the culture and remain mentally in their former professions. Still, it is central that they keep up this contact to be able to school the pupils into the environment of the trade in question, but also to help them to understand what skills a profession demands. However, the individual teacher also has to distance himself from the negative elements in the culture of the profession: patterns and habits that, for various reasons, have to be broken or changed. This paper draws attention to the ways in which a group of vocational teachers, who were participants in a project that aimed to train unauthorized vocational teachers, expressed their ambitions to prepare the pupils for a future professional career. When collecting information, we used the degree dissertations they produced and discussed in seminars, and informal dialogues. The result shows that it is important that the instruction location resembles a real working site as far as possible. These places are more or less realistic copies of a garage, a restaurant kitchen, a hairdressing salon, and so on, in order to give the pupils a realistic setting for instruction. However, the fact that these simulated workplaces lack the necessary support functions that exist in a company creates problems, problems which make a lot of extra work for the teachers. Vocational teachers also have to instruct the pupil in the experienced practitioner’s professional skills and working situation, but the pupil herself/himself must learn the job by doing it in practice. Some vocational upper secondary programs lack relevant course literature and the businesses give little support. This also makes extra work for the teachers. Moreover, the distance between the vocational programs and the trainee jobs was experienced as being difficult to overcome. One reason seems to be differences between businesses and differing preconditions between small and big companies’ abilities to take care of these pupils. The upper secondary school vocational programs also play a role in cementing existing gender roles, as well as perpetuating class-related patterns on the labour market.

How initial vocational education and training (IVET) teachers in Sweden perceive their prospects of being able to prepare upper secondary school pupils for a future occupation

Vocational teachers in Swedish upper secondary schools are a heterogeneous category of teachers, connected to different types of trade. These teachers represent a broad set of trade skills varying in content and character. In their teacher role, they continue to wear the clothes, speak the language, share the culture and remain mentally in their former professions. Still, it is central that they keep up this contact to be able to school the pupils into the environment of the trade in question, but also to help them to understand what skills a profession demands. However, the individual teacher also has to distance himself from the negative elements in the culture of the profession: patterns and habits that, for various reasons, have to be broken or changed. This paper draws attention to the ways in which a group of vocational teachers, who were participants in a project that aimed to train unauthorized vocational teachers, expressed their ambitions to prepare the pupils for a future professional career. When collecting information, we used the degree dissertations they produced and discussed in seminars, and informal dialogues. The result shows that it is important that the instruction location resembles a real working site as far as possible. These places are more or less realistic copies of a garage, a restaurant kitchen, a hairdressing salon, and so on, in order to give the pupils a realistic setting for instruction. However, the fact that these simulated workplaces lack the necessary support functions that exist in a company creates problems, problems which make a lot of extra work for the teachers. Vocational teachers also have to instruct the pupil in the experienced practitioner’s professional skills and working situation, but the pupil herself/himself must learn the job by doing it in practice. Some vocational upper secondary programs lack relevant course literature and the businesses give little support. This also makes extra work for the teachers. Moreover, the distance between the vocational programs and the trainee jobs was experienced as being difficult to overcome. One reason seems to be differences between businesses and differing preconditions between small and big companies’ abilities to take care of these pupils. The upper secondary school vocational programs also play a role in cementing existing gender roles, as well as perpetuating class-related patterns on the labour market.

Respostas dinâmicas em sistemas distribuídos e decomposição forçada da superfície livre para um modelo acoplado Oceano-Atmosfera

O objetivo deste trabalho é a introdução e desenvolvimento de uma metodologia analítico-simbólica para a obtenção de respostas dinâmicas e forçadas (soluções homogêneas e não homogêneas) de sistemas distribuídos, em domínios ilimitados e limitados, através do uso da base dinâmica gerada a partir da resposta impulso. Em domínios limitados, a resposta impulso foi formulada pelo método espectral. Foram considerados sistemas com condições de contorno homogêneas e não homogêneas. Para sistemas de natureza estável, a resposta forçada é decomposta na soma de uma resposta particular e de uma resposta livre induzida pelos valores iniciais da resposta particular. As respostas particulares, para entradas oscilatórias no tempo, foram calculadas com o uso da fun»c~ao de Green espacial. A teoria é desenvolvida de maneira geral permitindo que diferentes sis- temas evolutivos de ordem arbitrária possam ser tratados sistematicamente de uma forma compacta e simples. Realizou-se simulações simbólicas para a obtenção de respostas dinâmicas e respostas for»cadas com equações do tipo parabólico e hiperbólico em 1D,2D e 3D. O cálculo das respostas forçadas foi realizado com a determinação das respostas livres transientes em termos dos valores iniciais das respostas permanentes. Foi simulada a decomposição da resposta forçada da superfície livre de um modelo acoplado oceano-atmosfera bidimensional, através da resolução de uma equação de Klein-Gordon 2D com termo não-homogêneo de natureza dinâmica, devido a tensão de cisalhamento na superfície do oceano pela ação do vento.

Os efeitos da modalidade pregão na execução dos contratos continuados: um estudo de caso

O presente trabalho investiga os impactos das licitações do tipo menor preço, realizadas por meio de Pregão eletrônico, no desempenho das execuções dos contratos contínuos, efetivados pela Superintendência de Administração da AGU em Pernambuco - SAD/PE -, no período de 2006 a 2010. Teve como proposição a premissa de que a contratação do tipo menor preço pode, em função de suas próprias características, estimular uma redução excessiva nos preços ofertados pelos licitantes e originar contratações com valores muito baixos que interferem de forma negativa no desempenho da prestação dos serviços, gerando infrações contratuais e diminuindo a vida útil dos contratos contínuos. A aparente economia, consequência da acirrada competição nos leilões invertidos, que caracterizam a modalidade licitatória Pregão, em médio e longo prazo, pode ser questionada. Os resultados confirmaram a proposição, evidenciando um percentual de 55% dos contratos, oriundos de Pregão eletrônico, com infrações e 31%, rescindidos unilateralmente por descumprimento de cláusulas contratuais. Foi identificada uma relação, de força moderada, inversamente proporcional entre a economia inicial gerada na licitação e o tempo de execução dos contratos, sugerindo uma tendência no sentido de que - quanto maior a diferença entre o valor referencia e o contratado na licitação, menor o tempo de execução do contrato, pois, parte das contratações muito abaixo do preço de mercado, geraram contratos com pequena vida útil e com muitas infrações. As análises dos dados apontam para a necessidade de se relativizar a adoção da modalidade licitatória Pregão, repensando-se a sua indicação para serviços continuados

Eficiência da magic formula de value investing no mercado brasileiro

O objetivo deste trabalho é realizar procedimento de back-test da Magic Formula na Bovespa, reunindo evidências sobre violações da Hipótese do Mercado Eficiente no mercado brasileiro. Desenvolvida por Joel Greenblatt, a Magic Formula é uma metodologia de formação de carteiras que consiste em escolher ações com altos ROICs e Earnings Yields, seguindo a filosofia de Value Investing. Diversas carteiras foram montadas no período de dezembro de 2002 a maio de 2014 utilizando diferentes combinações de número de ativos por carteira e períodos de permanência. Todas as carteiras, independentemente do número de ativos ou período de permanência, apresentaram retornos superiores ao Ibovespa. As diferenças entre os CAGRs das carteiras e o do Ibovespa foram significativas, sendo que a carteira com pior desempenho apresentou CAGR de 27,7% contra 14,1% do Ibovespa. As carteiras também obtiveram resultados positivos após serem ajustadas pelo risco. A pior razão retorno-volatilidade foi de 1,2, comparado a 0,6 do Ibovespa. As carteiras com pior pontuação também apresentaram bons resultados na maioria dos cenários, contrariando as expectativas iniciais e os resultados observados em outros trabalhos. Adicionalmente foram realizadas simulações para diversos períodos de 5 anos com objetivo de analisar a robustez dos resultados. Todas as carteiras apresentaram CAGR maior que o do Ibovespa em todos os períodos simulados, independentemente do número de ativos incluídos ou dos períodos de permanência. Estes resultados indicam ser possível alcançar retornos acima do mercado no Brasil utilizando apenas dados públicos históricos. Esta é uma violação da forma fraca da Hipótese do Mercado Eficiente.